MEMS惯性传感器设计详解：理论与实践指南

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《惯性微机械(MEMS)：原理与实践》是一本实用且系统的指南，专为设计、制造和测试基于MEMS（微电子机械系统）的惯性传感器提供深入解析。该书旨在帮助读者将实际应用需求转化为可行的设计，并指导他们避开潜在的设计陷阱，缩短设计周期。书中详尽介绍了相关的基础知识，包括MEMS技术、封装、运动学和力学，以及传感器转换器的原理。作者Volker Kempe凭借超过40年的学术研究和工业开发经验，确保了内容的专业性和实用性。书中详细评估了不同的设计方法和架构，涵盖了关键的测试与校准环节。对于在现实世界中制造传感器所面临的实际挑战，作者提供了独特的见解，使得本书成为产业专业工程师、管理者、应用工程师以及希望全面了解该领域的学生们的宝贵资源。通过阅读本书，读者可以迅速掌握MEMS惯性传感器的核心技术，如如何选择合适的材料、设计微结构以实现高精度的加速度计或陀螺仪，以及如何优化传感器的动态性能。此外，书中还将讨论敏感元件的设计、信号处理算法以及噪声抑制策略，这些都是成功设计和实现高效、可靠惯性传感器的关键要素。《惯性微机械：原理与实践》不仅提供了理论基础，还结合了实践经验，使得无论是初入这个领域的学生还是已经在工业界从事惯性MEMS工作的专业人士，都能从中获益匪浅，提升他们的设计能力和对当前技术发展趋势的理解。这本书是惯性MEMS领域的一份权威参考，是推动科技创新和产品开发的重要工具。

xiv Preface

interesting not only for people working with inertial MEMS but also for every-

body who is looking for a general introduction into mechanical MEMS.

The following two main chapters are devoted to the two representatives of

inertial MEMS – accelerometers and gyroscopes. Here the focus is on the basic

principles, the methods and models to describe the dynamic behavior, and a

comprehensive presentation of diﬀerent approaches and architectures, including

their pros and cons. A short overview on test and calibration is added as a

separate chapter.

The book is written on an engineering level. Where possible, eﬀects and pro-

cesses are described analytically by mathematical models in order to impart a

feeling for the order of magnitude of diﬀerent eﬀects.

The book should be useful not only for specialists developing, manufacturing,

and using inertial sensors but also for people working in the application ﬁeld, for

product managers, and for sales people looking for background knowledge in their

area. The book can serve as a starting point for further academic investigations,

for instance in the area of shock-impact analysis of an entire packaged gyro,

including the eﬀect of signal processing.

In the experience of the author, many engineers, physicists, and mathemati-

cians are thankful for an exact but comprehensible presentation of the complex

and diﬃcult world of MEMS-based inertial sensors, where the eﬀects and models

behind the practical problems are reﬂected without improper simpliﬁcations or

phenomenological descriptions. The book is a modest attempt to meet some of

these challenges. Having worked with many specialists in the production, testing,

and design of inertial sensors, the author is convinced that the book can meet

actual needs, and hopes to elicit the broad interest of practitioners and scientists

in this area. For interested people, including students, the book may also serve

as an introduction to the world of mechanical MEMS.

Introduction

An inertial sensor is an observer who is caught within a completely shielded case

and who is trying to determine the position changes of the case with respect to

an outer inertial reference system.

Inertial sensors exploit inertial forces acting on an object to determine its

dynamic behavior. The basic dynamic parameters are acceleration along some

axis and the angular rate. External forces acting on a body cause an acceleration

and/or a change of its orientation (angular position). The rate of change of the

angular position is the angular velocity (angular rate). A speedometer is not an

inertial sensor because it is able to measure a constant velocity of a body that

is not exposed to inertial forces. An inertial sensor is unable to do so; however,

if the initial conditions of the body are known, their evolution can be calculated

by integrating the dynamic equation on the basis of the measured acceleration

and rate signals.

In the overwhelming majority of practical applications, such as vibrational

measurements, active suspension systems, crash-detection systems, alert systems,

medical activity monitoring, safety systems in cars, and computer-game inter-

faces, the short-term dynamic changes of the object are of interest. But there

are also many applications where inertial sensors are used for determination of

the positions and orientations of a body, as in robotics, general machine con-

trol, and navigation. Owing to the necessity of integrating the corresponding

dynamic equations, the accuracy requirements in these applications are usually

higher because the measurement errors and instabilities of the sensors are accu-

mulated over the integration time. Often inertial sensors are used in conjunction

with other measurement systems, as in the case of robotics, where they are used

together with position and force/torque sensors, or in the case of the integration

of Inertial Navigation Systems (INS) with Global Positioning Systems (GPS) in

cars. The accuracy of INS measurements can be improved signiﬁcantly by cor-

recting them with the GPS data using Kalman ﬁltering procedures. The INS can

then aid navigation even when the GPS is degraded or interrupted because of

jamming or interference.

1.1 A short foray through the pre-MEMS history

The history of inertial sensors is relatively short. Despite the fundamental role

played by inertial sensors in controlling the movement of a body, very little is

2 Introduction

known about early applications. This is even more remarkable given that most

of the ingredients for building acceleration and angular-rate sensors, such as ﬁne

mechanics and precise spring technologies, were available from the late Middle

Ages on and were used in the construction of, for instance, beautiful precision

clocks.

Accelerometers

One of the most likely reasons for the late appearance of acceleration sensors (or

“accelerometers” for short) was the lack of indicator technologies, or, in modern

phrasing, the lack of interfaces. This is certainly the reason why some former

applications of acceleration switches that needed only very simple mechanical

interfaces can be found. An acceleration switch initiated an action at a certain

level of acceleration, as in the activation of a detonator in some bombs during

the First World War.

The ﬁrst commercial accelerometer for broader application is credited to B.

McCollum and O. S. Peters and was developed around 1920 [

McCullom and

Peters 1924

]. It was based on a tension–compression resistance of a Wheatstone

half-bridge where the resistances were formed by carbon rings. The next techno-

logical step was the use of strain-gauge transducers starting from around 1938,

followed by the introduction of piezoelectric and piezoresistive transducers at

the end of the 1940s. These transducers could capture the forces caused by the

displacement of an elastically mounted mass within the sensor structure. Minia-

turization and the high robustness of this type of sensor paved the way for broad

applications in industry, terrestrial transport, aerospace, military uses, seismol-

ogy, science, and so on. The piezoelectric and piezoresistive transducer principles

were also among the ﬁrst to be employed at the beginning of the entry into the

world of inertial microelectromechanical systems (MEMS) – the world of the

combination of micrometer- and nanometer-scale mechanical elements, sensors,

actuators, and electronic circuits on one carrier or even on one chip. This entry

was prepared in the late 1970s, for instance with the demonstration of a batch-

fabricated silicon accelerometer with piezoresistive transducers. The silicon bulk

micromachined proof mass was bonded between two glass wafers [

Roylance and

Angell 1979

]. The commercialization of similar devices began around 10 years

later and was very soon based on a variety of available transducer principles such

as the sensing of capacitance changes between ﬁxed and movable plates, the fre-

quency measurement of resonant devices, the stabilization of a tunneling current

by a closed-loop system, the sensing of thermal changes between a heater and a

movable heat sink, and the sensing of changes of the thermal distribution within

an air bubble. This broad invasion of new and old ideas in the world of micro-

electronic technologies has opened the way to inexpensive mass applications of

inertial sensors in industry, cars, medicine, consumer goods, and so on.

Everybody knows the pioneering role of MEMS-based 50g accelerometers used

in airbag ignition devices, which became the ﬁrst high-volume product in the area

of inertial MEMS. It was especially encouraging that within these successful high-

volume products an example of the full monolithic integration of sensor and

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PhilipChen

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